I want a Daemon Prince! How to get Dark Apotheosis with Dark Apostles

The Chaos Boon table is a thing of beauty. The two Glaring Possiblities are Dark Apotheosis and Spawnhood. With a Dark Apostle or the re-roll boon Warlord trait you have a much better possibility of getting something good. How much better though?

At least 1 Dark Apostle pictured

With the re-roll you want to avoid Spawnhood (usually) and want to gain Dark Apotheosis (usually). To get either is a 1/18 chance. Now, if you're a lowly little Cultist with an autogun Spawnhood is actually the second best deal for you. You're gonna want to re-roll something like Fleet or +1 BS to hope that you can get upgraded to a disgusting gibbering mass of tentacles. If you're Aba-Aba-Abaddon you're already waaaay better than both a Daemon Prince and a Spawn so you'll want to re-roll both. To simplify math we'll see how probable it is for a Sarge in pretty Power Armor to get Dark Apotheosis, avoid Spawnhood and avoid Unworthy Offering (aka nothing).

The chance of you getting nothing are 1/6. You don't want to get Spawnhood either so your avoiding 2/9 possibilities. With a re-roll you have a 5% chance of getting either again. Though now with re-roll your chances of getting an unwelcome Spawnhood drop to 1/324 or .3%. Nice.

If you're just blind re-rolling for Dark Apotheosis you have a 1/18 chance at first but on your second attempt you also have that chance. Your chances of either of 2 rolls being Daemon Prince are thus ~11%. Awesome! You've effectively doubled your chances from before (obviously).

With this re-roll on hardier units like Typhus and Abaddon you've reduced your total chance of unwelcome Daemonhood or Spawnhood to 1.2%. An extremely low probability. You can now roll in peace with the beautiful Dark Apostle guiding your evil hand.

Side Note: Equip your Sarges with something to kill if you want constant boons. The best non-artifact combo is Lightning Claw and Power Axe. This lets you rip though anything less than power armor at initiative and also let's you have a good chance of wounding Termies with the Power Axe. You'll obviously not do well against melee monsters but most of those will hopefully cost more than you. The combo itself costs 40 points or roughly 2 MEQs for a lot of killing power. If you aren't worried about Termies just drop the Axe and challenge away.

Conclusion
Dark Apostles rule.